Question: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 7x + 6$ and $ BC = 8x + 4$ Find $AC$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {7x + 6} = {8x + 4}$ Solve for $x$ $ -x = -2$ $ x = 2$ Substitute $2$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 7({2}) + 6$ $ BC = 8({2}) + 4$ $ AB = 14 + 6$ $ BC = 16 + 4$ $ AB = 20$ $ BC = 20$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {20} + {20}$ $ AC = 40$